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Evaluate the definite integral.

$ \displaystyle \int^1_0 \sqrt[3]{1 + 7x} \, dx $

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01:36

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 5

The Substitution Rule

Integration

Missouri State University

Harvey Mudd College

Boston College

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

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1.7 Next to the 1/3 DX and I were looking at the integral from 01 We know we can divine are you? And then we can define our d acts. VX is do you over seven. Given this, we can now write or integral in terms of you. And now the upper limit is going to be you is one plus sometimes one, which is eight. So we now have the integral from 1 to 8. Okay, let's pull up the constant, which is 1/7. Yeah, and now we know that we can use the power rule which is increased the expert it by one and divide by the new exponents. And now we're climb a fundamental theme of calculus by plugging end our bounds to get 45 over 28.

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